A370934 Expansion of e.g.f. (1/x) * Series_Reversion( x*(4 - exp(3*x))/3 ).

1, 1, 7, 84, 1497, 35676, 1067931, 38548980, 1630600677, 79132611420, 4334891782095, 264625534657188, 17815224081030129, 1311349332273617196, 104778837463344022179, 9031998822763725245268, 835500403485829779202557, 82557790782397502710806396

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Index entries for reversions of series

Formula

a(n) = (1/(n+1)!) * Sum_{k=0..n} 3^(n-k) * (n+k)! * Stirling2(n,k).

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(4-exp(3*x))/3)/x))
(PARI) a(n) = sum(k=0, n, 3^(n-k)*(n+k)!*stirling(n, k, 2))/(n+1)!;

Crossrefs

Cf. A052894, A370894.

Cf. A258923.

Sequence in context: A034323 A172455 A258174 * A254569 A183177 A367351

Adjacent sequences: A370931 A370932 A370933 * A370935 A370936 A370937

Keyword

nonn

Author

Seiichi Manyama, Mar 06 2024

Status

approved